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The variational iteration method: an efficient scheme for handling fractional partial differential equations in fluid mechanics. (English) Zbl 1189.65254

Summary: Variational iteration method has been used to handle linear and nonlinear differential equations. The main property of the method lies in its flexibility and ability to solve nonlinear equations accurately and conveniently. In this work, a general framework of the variational iteration method is presented for analytical treatment of fractional partial differential equations in fluid mechanics. The fractional derivatives are described in the Caputo sense. Numerical illustrations that include the fractional wave equation, fractional Burgers equation, fractional KdV equation, fractional Klein-Gordon equation and fractional Boussinesq-like equation are investigated to show the pertinent features of the technique. Comparison of the results obtained by the variational iteration method with those obtained by Adomian decomposition method reveals that the first method is very effective and convenient. The basic idea described in this paper is expected to be further employed to solve other similar linear and nonlinear problems in fractional calculus.

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
26A33 Fractional derivatives and integrals
76A02 Foundations of fluid mechanics
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